Nowadays, the correspondence between an anti-de Sitter spacetime
and a conformal field theory living on its boundary (AdS/CFT) is
the well-known holographic picture of the world. This
correspondence provides a method for relating a strongly
interacting field theory to a dual classical gravity
[1]}, [2]}, [3]}. It was shown that by employing the
dictionary of AdS/CFT duality, one can relate the observed
properties in the AdS bulk to their corresponding quantities in
CFT on the boundary. An interesting application of this duality
was recently proposed by Hartnoll, et. al., [4]}, [5]} who
showed that some properties of strongly coupled superconductors
can be potentially described by a classical general relativity
living in one higher dimension. The motivation for this study is
to shed some light on the problem of understanding the mechanism
of the high temperature superconductors in condensed matter
physics. Following [4]}, [5]}, a lot of works have been
appeared which attempt to investigate the holographic
superconductors from different perspective [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}.
Focusing on the simplest form by working in the probe
approximation, in which the scalar and gauge fields backreaction
effects on the gravity sector can be ignored and fixing the metric
as static, the authors of [14]} employed the SL
variational method as an analytic approach for calculating the
properties of the holographic superconductors. They discussed
analytic approximations to the solutions of the nonlinear field
equations both near the critical temperature \(T_{c}\)  and in the
low temperature limit \(T \rightarrow 0\) . The critical temperature
and critical exponent and other quantities for different modes of
superconductors including \(s\) -wave, \(p\) -wave and \(d\) -wave, were
also investigated in the probe limit [23]}, [24]}, [25]}, [26]}, [27]}.
